Introduction
Electrical conductivity of an aqueous solution depends on how many charge carriers (ions) are present and how freely they move. When you dissolve salts, acids, or bases in water, they dissociate into ions that can carry electric current. The more ions, the higher the electrical conductivity, and the greater the ion mobility, the more efficiently the solution conducts.
- Degree of dissociation – strong electrolytes (e.g., NaCl, HCl, NaOH) dissociate completely, weak electrolytes (e.g., acetic acid, NH₄Cl) only partially.
- Concentration of ions – a 0.1 M solution contains ten times more ions than a 0.01 M solution of the same electrolyte.
- Ionic mobility – small, highly charged ions (H⁺, OH⁻) move faster than larger, less charged ones (Cl⁻, SO₄²⁻).
By examining these variables, we can place any group of aqueous solutions in a clear order from lowest to highest conductivity. The following sections walk through the scientific background, present a step‑by‑step ranking method, and finally list the solutions in their correct order Simple, but easy to overlook..
Scientific Background
1. Electrolytes and Their Classification
| Type of electrolyte | Example | Dissociation in water | Conductivity trend |
|---|---|---|---|
| Strong acid | HCl, H₂SO₄ | Complete → H⁺ + Cl⁻ (or HSO₄⁻/SO₄²⁻) | Very high |
| Strong base | NaOH, KOH | Complete → Na⁺ + OH⁻ | Very high |
| Strong salt | NaCl, K₂SO₄ | Complete → Na⁺ + Cl⁻ (or K⁺ + SO₄²⁻) | High |
| Weak acid | CH₃COOH, H₂CO₃ | Partial → CH₃COO⁻ + H⁺ (small fraction) | Moderate to low |
| Weak base | NH₃ (as NH₄OH) | Partial → NH₄⁺ + OH⁻ | Moderate to low |
| Nonelectrolyte | Glucose, sucrose | No ions | Negligible |
It sounds simple, but the gap is usually here.
A strong electrolyte yields the maximum possible ion concentration for a given molarity, while a weak electrolyte contributes far fewer ions because only a fraction dissociates And that's really what it comes down to..
2. Molar Conductivity (Λₘ) and Specific Conductivity (κ)
- Specific conductivity (κ), measured in S · cm⁻¹, is the conductance of a solution of a defined cell length and cross‑section.
- Molar conductivity (Λₘ) = κ / c (where c is molar concentration). Λₘ reflects ion mobility; it increases as concentration decreases because inter‑ionic interactions weaken.
For ranking purposes, we usually compare specific conductivity at the same temperature (often 25 °C) and similar concentrations, because κ directly indicates how well the solution conducts electricity.
3. Ionic Mobility
The limiting molar conductivity (λ⁰) of individual ions at infinite dilution is a tabulated constant. At 25 °C:
- H⁺ ≈ 349.8 S · cm² · mol⁻¹ (the highest due to the Grotthuss mechanism)
- OH⁻ ≈ 199.1 S · cm² · mol⁻¹
- Na⁺ ≈ 50.1 S · cm² · mol⁻¹
- Cl⁻ ≈ 76.3 S · cm² · mol⁻¹
- SO₄²⁻ ≈ 160 S · cm² · mol⁻¹
When a solution contains H⁺ or OH⁻, its conductivity spikes, even at modest concentrations Simple as that..
Step‑by‑Step Ranking Procedure
Assume we are given the following aqueous solutions (all prepared at 0.01 M unless stated otherwise):
- 0.01 M NaCl (strong salt)
- 0.01 M CH₃COOH (weak acid)
- 0.01 M KCl (strong salt)
- 0.01 M NH₄Cl (strong salt, but contains NH₄⁺)
- 0.01 M HCl (strong acid)
- 0.01 M NaOH (strong base)
- 0.01 M MgSO₄ (strong salt with divalent ion)
- 0.01 M C₆H₁₂O₆ (glucose, nonelectrolyte)
Step 1 – Identify electrolyte strength
- Strong electrolytes: NaCl, KCl, NH₄Cl, HCl, NaOH, MgSO₄.
- Weak electrolyte: CH₃COOH.
- Nonelectrolyte: glucose.
Step 2 – Count the total number of ions produced per formula unit
| Solution | Dissociation equation | Ions per formula unit |
|---|---|---|
| NaCl | NaCl → Na⁺ + Cl⁻ | 2 |
| KCl | KCl → K⁺ + Cl⁻ | 2 |
| NH₄Cl | NH₄Cl → NH₄⁺ + Cl⁻ | 2 |
| HCl | HCl → H⁺ + Cl⁻ | 2 (but H⁺ has very high mobility) |
| NaOH | NaOH → Na⁺ + OH⁻ | 2 (OH⁻ high mobility) |
| MgSO₄ | MgSO₄ → Mg²⁺ + SO₄²⁻ | 2 (each ion carries double charge) |
| CH₃COOH | CH₃COOH ⇌ CH₃COO⁻ + H⁺ (≈ 1 % dissociation) | ≈ 0.02 (effectively 0) |
| Glucose | No dissociation | 0 |
All strong electrolytes generate two ions, but the charge magnitude and ionic mobility differ Not complicated — just consistent..
Step 3 – Evaluate ion mobility and charge
- H⁺ and OH⁻ dominate conductivity.
- Mg²⁺ and SO₄²⁻ have higher λ⁰ than monovalent Na⁺ or Cl⁻, but the increase is modest compared with H⁺/OH⁻.
- NH₄⁺ mobility (≈ 73 S · cm² · mol⁻¹) is similar to K⁺.
Step 4 – Estimate specific conductivity (κ)
A simplified proportionality:
κ ∝ Σ (cᵢ · λ⁰ᵢ)
where cᵢ is the molar concentration of each ion. Because all solutions have the same overall concentration (0.01 M), the ranking reduces to comparing the sum of λ⁰ values for the ions present Worth keeping that in mind..
| Solution | λ⁰ (H⁺) | λ⁰ (OH⁻) | λ⁰ (Na⁺) | λ⁰ (K⁺) | λ⁰ (NH₄⁺) | λ⁰ (Cl⁻) | λ⁰ (Mg²⁺) | λ⁰ (SO₄²⁻) | Σ λ⁰ (approx.) |
|---|---|---|---|---|---|---|---|---|---|
| HCl | 349.Plus, 8 | – | – | – | – | 76. 3 | – | – | 426 S · cm² · mol⁻¹ |
| NaOH | – | 199.That's why 1 | 50. Also, 1 | – | – | – | – | – | 249 S · cm² · mol⁻¹ |
| MgSO₄ | – | – | – | – | – | – | 119. 0* | 160 | 279 S · cm² · mol⁻¹ |
| NaCl | – | – | 50.1 | – | – | 76.Here's the thing — 3 | – | – | 126 S · cm² · mol⁻¹ |
| KCl | – | – | – | 73. 5 | – | 76.And 3 | – | – | 149. 8 S · cm² · mol⁻¹ |
| NH₄Cl | – | – | – | – | 73.5 | 76.Think about it: 3 | – | – | 149. 8 S · cm² · mol⁻¹ |
| CH₃COOH | 349.8 × 0.And 01 ≈ 3. 5 | – | – | – | – | – | – | – | **≈ 3. |
*Mg²⁺ λ⁰ ≈ 119 S · cm² · mol⁻¹ (average of literature values).
Step 5 – Rank from lowest to highest κ
- Glucose solution – no ions, κ ≈ 0.
- 0.01 M CH₃COOH – weak acid, minimal ion production.
- 0.01 M NaCl – moderate conductivity (both ions have modest mobility).
- 0.01 M KCl ≈ 0.01 M NH₄Cl – slightly higher than NaCl because K⁺/NH₄⁺ are a bit more mobile than Na⁺.
- 0.01 M MgSO₄ – presence of divalent ions raises Σ λ⁰ above the monovalent salts.
- 0.01 M NaOH – OH⁻ contributes a large mobility term.
- 0.01 M HCl – H⁺ is the fastest ion; this solution exhibits the highest conductivity among the list.
Detailed Discussion of Each Solution
1. Glucose (C₆H₁₂O₆) – the baseline
Glucose dissolves as intact molecules; it does not generate charge carriers. 5 × 10⁻⁶ S · cm⁻¹ at 25 °C). This means its specific conductivity is essentially the same as that of pure water (≈ 5.This makes it the lowest‑conductivity member of any aqueous set that includes an organic nonelectrolyte Practical, not theoretical..
2. Acetic Acid (CH₃COOH) – a weak acid
Acetic acid’s dissociation constant (Kₐ ≈ 1.Even so, 8 × 10⁻⁵) means that at 0. 01 M only about 1 % of the molecules release H⁺ and CH₃COO⁻. The resulting ion concentration (~1 × 10⁻⁴ M) is too low to produce a noticeable conductivity, yet it is still higher than pure water. The presence of a tiny amount of H⁺ gives it a slightly higher κ than glucose but far below any strong electrolyte.
3. Sodium Chloride (NaCl) – classic strong electrolyte
NaCl completely dissociates into Na⁺ and Cl⁻. Both ions have moderate mobilities, and the solution’s conductivity at 0.That's why 01 M is roughly 1. 2 × 10⁻³ S · cm⁻¹. This value is often used as a reference point in laboratory conductivity meters Small thing, real impact..
4. Potassium Chloride (KCl) and Ammonium Chloride (NH₄Cl) – comparable conductors
K⁺ (λ⁰ ≈ 73.5) and NH₄⁺ (λ⁰ ≈ 73.5) are a bit more mobile than Na⁺, while Cl⁻ remains the same. Here's the thing — the net effect is a ~20 % increase in conductivity over NaCl at the same concentration. Because their ionic mobilities are nearly identical, KCl and NH₄Cl rank together Not complicated — just consistent..
5. Magnesium Sulfate (MgSO₄) – influence of divalent ions
Mg²⁺ carries twice the charge of Na⁺, and SO₄²⁻ also carries a double charge. Although the larger ionic radius reduces mobility compared with monovalent ions, the charge factor amplifies conductivity: each ion contributes twice the current per mole. Hence, MgSO₄’s κ exceeds that of the monovalent salts, sitting between NaOH and the strong acid solutions.
6. Sodium Hydroxide (NaOH) – the strong base
NaOH yields Na⁺ (moderate mobility) and OH⁻ (high mobility, λ⁰ ≈ 199). The presence of OH⁻ pushes the conductivity well above the monovalent salts but still below HCl because OH⁻ is less mobile than H⁺ Turns out it matters..
7. Hydrochloric Acid (HCl) – the champion of conductivity
HCl’s complete dissociation produces H⁺, the fastest ion in aqueous media, and Cl⁻. The combined λ⁰ sum is the highest among the listed solutions, giving HCl the greatest specific conductivity at equal molarity.
Frequently Asked Questions
Q1. Does concentration always dominate conductivity?
A: At a given temperature, increasing concentration raises the number of charge carriers, thus increasing κ. Even so, beyond a certain point (≈ 0.1 M for many salts), ion pairing and increased viscosity reduce ion mobility, causing κ to rise more slowly or even plateau. For the low concentrations used in the ranking (0.01 M), κ scales linearly with concentration.
Q2. Why do divalent ions sometimes give higher conductivity despite lower mobility?
A: Conductivity depends on charge (z) as well as mobility (u). The molar conductivity contribution of an ion is λ = z · F · u, where F is Faraday’s constant. Doubling the charge roughly doubles the contribution, offsetting the modest loss in mobility.
Q3. Can temperature change the order?
A: Yes. Raising temperature enhances water’s dielectric constant and reduces viscosity, increasing ion mobility for all species. The relative order usually stays the same, but the gaps between solutions widen. At very high temperatures (near boiling), weak electrolytes dissociate more, slightly boosting their conductivity Small thing, real impact..
Q4. How does the Grotthuss mechanism affect H⁺ mobility?
A: The Grotthuss mechanism describes rapid proton hopping through a hydrogen‑bond network, allowing H⁺ to move far faster than any other ion of comparable size. This is why even dilute HCl solutions conduct exceptionally well That alone is useful..
Q5. Are there exceptions where a weak electrolyte outranks a strong one?
A: Only when the weak electrolyte is at a much higher concentration than the strong electrolyte. As an example, 1 M acetic acid (partially dissociated) can have a higher κ than 0.01 M NaCl because the sheer number of molecules compensates for low dissociation.
Conclusion
Ranking aqueous solutions by electrical conductivity hinges on three intertwined concepts: electrolyte strength, ion concentration, and ionic mobility. By dissecting each solution into its constituent ions, assigning the appropriate limiting molar conductivities, and summing the contributions, we obtain a clear hierarchy:
Glucose < Acetic acid < NaCl < KCl ≈ NH₄Cl < MgSO₄ < NaOH < HCl That's the whole idea..
Understanding this order equips students, laboratory technicians, and engineers with the ability to predict how a solution will behave in conductivity‑based measurements, electrochemical cells, or water‑quality monitoring. On top of that, the same analytical framework can be extended to any set of aqueous solutions—simply identify the ions, note their mobilities, and consider concentration and temperature. Armed with these tools, you can confidently interpret conductivity data and make informed decisions in chemistry, environmental science, and industry Which is the point..
